Instability due to the dust-particulate–phonon interaction

Interactions of dust particulates and phonons in a plasma are studied from a quantum mechanical viewpoint. An attraction between negatively charged dust particulates due to a stable wake potential behind a dust particulate in the supersonic ion flow is shown to be the result of exchanging phonons between the dust particulates. A collection of dust particulates becomes hydrodynamically unstable when the ion flow becomes subsonic. The growth rate of the instability is given by $\gamma =0.87\mathrm{}\hspace{0.5em}({\mathrm{\omega }}_{\mathrm{pi}}{/2\mathrm{}\mathrm{\omega }}_{\mathrm{pd}}{)}^{1/3}{\Omega }_{\mathbf{k}},$ where ${\omega }_{\mathrm{pi}}$ is the ion plasma frequency, ${\omega }_{\mathrm{pd}}$ is the dust plasma frequency, and ${\Omega }_{\mathbf{k}}$ is the dust acoustic frequency.